Non-Markovian Quantum Decay in Complex Environments: A Hyperstatistical Approach
Year: 2026
Type: preprint
Abstract: The exponential decay of an unstable quantum state, as described by standard Markovian theories such as Fermi's Golden Rule, assumes a simple, structureless environment. However, in complex environments characterized by disorder, long-range interactions, or strong fluctuations, local decay rates fluctuate, leading to non-Markovian dynamics and power-law ``long-time tails.'' In this paper, we apply the recently proposed \textit{hyperstatistics} framework to the problem of quantum decay in such complex environments. By considering a $γ$-distribution of local decay rates across mesoscopic domains, we derive a macroscopic survival probability governed by a $q$-exponential function. We then use the $q$-generalized Gamma function, defined via the Mellin transform of the $q$-exponential, to calculate the moments of the decay-time distribution. We show that the mean quantum lifetime is $\langle t\rangle = \int_0^\infty P(t)\,dt= [\langleΓ\rangle(2-q)]^{-1},$ and is therefore finite for $q<2$. The convergence of the second moment, and hence of the lifetime variance, instead requires the stricter condition $q<3/2$. These results provide a refined physical interpretation: for $1
Source: arXiv (Cornell University)
Author: Fabiano, Nicola
Institutions: University of Belgrade, Vinča Institute of Nuclear Sciences
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214010917
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